New approaches to modeling the dynamics of misaligned beams in nonlinear gradient waveguides

The propagation of a misaligned paraxial beam through a nonlinear waveguide medium can be presented as a nonlinear dynamical problem, where the longitudinal coordinate z plays the role of time, while the transverse pattern of the field is the dynamical system evolving with z. The reduction to a finite-dimensional system is possible within the framework of the approximate method using Gaussian probe functions whose parameters are determined by Galerkin's criterion in the basis of a small number of flexible Gaussian modes. This method is referred as the modified generalized method of moments (MGMM). Using the MGMM we studied the dynamics of an off-axis initially Gaussian beam propagating through a Kerr nonlinear parabolic waveguide and revealed stationary, periodic and quasiperiodic regimes, as well as nontrivial phenomena, such as phase locking, cycle generation, etc. In particular, the behavior of the beam variables in the vicinity of the stationary states was analyzed. However, direct numerical modeling shows significant non-Gaussian distortions of the beam caused by Kerr nonlinearity, so MGMM is expected to describe correctly the dynamics of the beam moments rather than the field transverse pattern itself. To check this idea alternative approaches are desirable. The method proposed here involves the exact numerical calculation of nonlinear modes followed by the linear analysis of small nonstationary perturbations of these modes based on Bogoliubov's equations.